Return Distribution Choices for Monte Carlo VaR and CVaR

Summary

The document asks whether asset log returns must follow a normal distribution when calculating VaR and CVaR with Monte Carlo simulation and volatility estimated using the Heston model. The response describes prior market-factor simulations in which historical returns showed skewness, kurtosis, and higher moments inconsistent with normality. It notes that Johnson distributions were tried as an alternative family.

The account says the work was abandoned for several reasons, including regulatory comparability: Basel II required VaR calculations to follow methods that could be compared across institutions, even when those methods were not considered optimal. This provides a practical caution that distribution choice may be shaped by reporting rules as well as statistical fit. However, the response does not establish a general distribution requirement for Heston-based simulation, detail how to fit or validate alternatives, or report a comparison of risk estimates. It is an anecdotal illustration rather than a complete modeling guide.

Key ideas

• The response describes historical market-factor returns with skewness and kurtosis beyond a normal distribution.
• Johnson distributions were considered as an alternative for Monte Carlo VaR work.
• Regulatory comparability requirements can constrain the methods used to calculate VaR.
• The anecdote does not specify a universal return distribution requirement for Heston simulations.

Tags

# Log-Return Distribution Assumptions in VaR and CVaR Calculation Using Monte Carlo Simulation with the Heston Model


# Log-Return Distribution Assumptions in VaR and CVaR Calculation Using Monte Carlo Simulation with the Heston Model












I want to calculate VaR and CVaR using Monte Carlo simulation and by estimating volatility with the Heston model. Do the asset log-returns have to be normally distributed? Because I haven't found any references stating that log-returns must be normally distributed.

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/82174

A long time ago I worked on Monte Carlo VaR of market factors where the historical returns were clearly not normally distributed, but rather had non-normall skewness, kurtosis, and even higher moments. We tried Johnson distributions in particular. We gave up for a variety of reasons, in particular because for Basel II, the regulators wanted everyone to calculate VaRs in ways that weren't necessarily "the best", but would be comparable to others.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.